A comprehensive study of two-phase flow in deformable porous media

This study explored the initial-boundary value problem of an immiscible, incompressible two-phase flow within a deformable porous medium system, modeled in an N-dimensional (N≥3) Euclidean space. The primary objective was to devise a novel model that effectively captured previously overlooked physical phenomena and established the global existence of a weak solution to the system. After proving the existence of a classical solution to the approximate problem using Schauder's fixed point theorem under a series of reasonable assumptions, we obtained the convergence to a weak solution of the original problem in two different cases by applying the Fréchet–Kolmogorov theorem. Subsequently, we verified the applicability of this model to the commonly used van Genuchten model in the dynamic simulation of oil storage, providing theoretical support for engineering applications.